Yeah so, you obviously need to eat more. If I understand you correctly you fast for 24 hours per day, which in itself is fine, however it is VERY hard to get one day worth of food in one meal. Especially vegetarian meal.
So you need at least one more meal per day, maybe even two more to get into caloric surplus. Think of it this way. To maintain your current weight you need to eat around 1200-1300 kcal/day, you would probably want to be around 1800kcal/day to start adding weight. I would guess you currently eat well below 1200kcal per day. So if you take you current portion size and just eat that amount once more every day you will at least hold your weight and probably gain some. If you are still not adding weight after a couple of weeks, add one more meal.
On a pure plantbased vegan diet I would recommend you start stocking up on beans, lentils and nuts since it is full of protein and is fairly energy dense. Include that in you every meal. Prepare food to eat the next day at the same time you eat your dinner, then just bring that with you to college.
Make a plan with times when you are going to eat your meals and be punctual with your meal time. You will feel stuffed the first couple of weeks, but make sure to eat your meals even if you have to divide it into smaller portions. If you keep to your new meal plan and eat at the same time every day, after a couple of weeks you will get hungry at that time and eating your meals will be easier.
With a lowered immune system I would not recommend you start exercising right now, it will just make you ill. So start with fixing your energy intake. Then after a while you might want to take up some weight training to gain some muscles.
You should also concider going to a doctor, not only for a check up on your overall health but also so a professional can determin if you need to be referred to a weight clinic or any other problems which can't be determined on a forum like this.
